PAP Algebra 2
Rational Exponents & Radicals Test Review
1.
Write each expression in radical form.
1
a) (10x ) 3
2.
Name: _____________________
3
3
b) −2 4
c) ( −2 ) 4
d) 8m 4 + 3k 2
(
)
2
3
−
Simplify each radical expression.
a)
a 4 b5 c 7
d) 5 81x4 y 2 • 5 6 x2 y3
g)
x2 + 2 x + 1
j) 2 3 5x7 + 3x 3 40 x4
m)
9
2 + 11
p)
32 x 5
27 x 3
r)
( 81 )
4
−2
b)
e)
h)
x 4 n y 3n + 2
3
3
−54
f)
5
−
i)
9c3
l)
27c5
n)
s)
3
320
3
5
k)
q)
x 2 • 4 x3
c)
3
( a + 7b )
a2n
a7n
4
5
2
4
o)
8 54
•
27
9
27
4
9
ab3c
3
(
a 2b 3c
6•36
6
)
u) The expression 4ab 2b − 3a 18b3 + 7ab 6b is equivalent to
a. 2ab 6b
3.
b. 16ab 2b
c. −5ab + 7ab 6b
d. −5ab 2b + 7ab 6b
Evaluate each expression.
a) 64
2
3
b) −5 ( 216 )
2
3
c) ( −32 )
−
⎛ 1 ⎞
d) ⎜
⎟
⎝ 512 ⎠
3
5
−
2
3
Simplify each expression
3
4
e) k • k
2
5
⎛ b5 ⎞
f) ⎜
−10 ⎟
⎝ 32a ⎠
5
⎛ 23
⎞
g) b ⎜ b − b 2 ⎟
⎝
⎠
j)
x
2
5
⎛ m − 8 5
h) ⎜ − 2
⎜ t 7
⎝
1
2
3
−
2
⎞
⎟
⎟
⎠
4
⎛ t 16
⎜ 1
⎜ m 5
⎝
⎛ y − x ⎞
k) ⎜
⎟
⎝ xy − 9 ⎠
5
6
x 5 • x −5
⎞
⎟
⎟
⎠
2
−4
i)
250 3
2
23
⎛ ⎛ 116
2x
l) ⎜ ⎜ 4
⎜⎜ ⎜ x 3
⎝ ⎝
0
⎞
⎟
⎟
⎠
2
⎞
⎟
⎟⎟
⎠
−3
1
m) a
4.
72
•a
5
⎛
⎞ 3
2
8
x
y
⎟
n) ⎜
1
⎜
⎟
⎜ 27 x 2 y ⎟
⎝
⎠
50
o)
Simplify each expression. Assume all variables are positive.
a) − z 2 16 z 3 + 3 36 z 7
1
⎛ 13
⎞
d) ⎜ 3a − 2a 2 ⎟
⎝
⎠
b) 4 + x 3 − 2 x
(
2
e)
)(
3− x
x
4
3
1
2
)
⎛ − 14 ⎞
x ⎜ x ⎟
⎝
⎠
( )
3
2
Solve each equation.
5.
a) 3x5 + 350 = −379
6.
Solve each equation. When solving a radical equation, be sure to check for
extraneous solutions.
a) x − 2 = 2 x − 1
4
b) ( x + 4 ) = 625
b)
3
3x − 3 = 3 4 x + 6
c) 4 x = 9 x + 9
3
d)
x +3= 0
e) 2 x + x = 3
f)
( x + 3) 2 − 1 = 7
2
g)
4 x + 5 = 10 x − 1 − 2
3
h) 4( x − 5) − 2 = 62
4
k) (3x − 2) − 40 = 41
For 17-19, given the functions, evaluate the following expressions.
17.
f(x) = x2 – 4 and g(x) = 4x – 1
a) f [g(3)]
18.
f (x) = x 2 + 2 and g(x) = − 3x
a) f [g(8)]
b) f(g(x))
−1
3
b) g [f(5)]
19. f ( x) = 2 x − 3 and g ( x) = 2 x 2 − x − 3
a) f ( x) − g ( x)
b) f (−1) − g (−1)
Perform the indicated operations. Answer in SIMPLEST form. BOX ANSWERS. (3 pts.
each)
20. Given f ( x) = 5 x3
f ( x)
a)
=
g ( x)
and g ( x) = 2 x
1
2
b)
f (x)ig(x)
c) f(g(x))
21. (each part is 2 pts.) Given the graph y = f ( x) below with the point (-1, -1) as a point of
inflection, find
a. f (−3) − f (4)
6
4
2
−6 −4 −2
−2
−4
−6
−8
b. f (−5)
2
4
6
8 10
c. f −4